Les systèmes de preuves formelles ont connu ces dernières années des évolutions importantes. Des travaux récents, comme la preuve formelle du théorème des quatre couleurs ou celle du théorème des nombres premiers, ont montré que ces systèmes ont atteint un niveau de maturité leur permettant de s'attaquer à des problèmes mathématiques non triviaux. Malgré cela, l'utilisation des systèmes de preuves formelles en mathématique reste très limitée. Un des arguments qui est avancé pour expliquer cette situation est le manque de bibliothèques de preuves formelles. Cette thèse s'intéresse au développement de composants mathématiques pour la théorie des groupes finis. Elle entre dans le cadre du travail de formalisation du théorème de Feit-Thompson sur la classification des groupes finis. L'objectif principal dans ce travail est d'appliquer les techniques de génie logiciel pour faciliter la réutilisation et l'organisation des développements mathématiques formelles de grande échelle, comme la formalisation du théorème de Feit-Thompson. Cette thèse présente une première formalisation du théorème de Cayley-Hamilton sur les polynômes et les matrices. Elle présente aussi des développements sur la théorie des représentations des groupes finis qui est une composante nécessaire à la formalisation de la preuve du théorème de Feit-Thompson. En particulier, elle présente une formalisation de la théorie des modules sur un corps ou sur une algèbre ainsi qu'une formalisation du théorème de Maschke. Ces développements ont été faits dans le système Coq et avec l'extension SSReflect.

There are over one thousand closed ‘small’ landfills in Ontario, each with differing circumstances and potential problems. This project proposes a method of addressing such dormant sites in situ, based upon a case study in Hamilton. Of the four closed landfills within Hamilton city limits, three of them lie in the low lands of the Red Hill Creek Valley. Perched at the source of the Red Hill Creek, the Upper Ottawa Street Landfill introduces unspoken toxins into the ecosystem of the entire valley. As the storm water catchment for the escarpment watershed, the creek serves a critical role in the recreational green belt which divides Hamilton and Stoney Creek. The source of this creek must be celebrated, not fenced off from public access due to landfill hazards. This proposal investigates beyond material recovery, into the possibilities of resource, ecosystem, and community recovery. Landfill mining, material sorting, and power generation through incineration are employed to reduce landfill volume. As the landfill is consumed, a new landscape is constructed, providing improved flood-prevention at the creek and a sanitary lined landfill for those materials remaining on site. Creek, forest, and field habitats are restored on site without the threat of contamination from landfill contents. The public can safely view the landfill mining operations from an elevated walkway, having new experiences with every visit. As the boundaries of the closed landfill are stripped away, the source of the Red Hill Creek and the new recreational parkland are made publicly accessible. Using this design as a reference, the equipment and operations designed for this site can be developed into a province-wide proposal.

Ce travail s'inscrit principalement dans le domaine de synthèse d'observateurs pour des synthèses non linéaires. D'une part le développement d'une nouvelle méthodologie de synthèse est proposée et d'autre part des résultats supplémentaires pour les observateurs à horizon glissant sont donnés. La première partie est plus directement dédiée aux rappels des notions de base d'observabilité des systèmes linéaires et non linéaires, ainsi qu'à la description des principales techniques de synthèse d'observateurs. De cette étude, il a été possible d'énoncer les avantages et les inconvénients de chaque méthode. Dans une deuxième partie et grâce à l'étude des différentes techniques de synthèse, une nouvelle méthodologie de synthèse d'observateur pour des systèmes non linéaires a été développée. Cette méthodologie divise un systhème en [n] problèmes d'optimisation scalaires, dénommés problèmes élémentaires, qui peuvent être résolus en parallèle en utilisant un solveur numérique de l'équation de Hamilton-Jacobi sclaire que pour de systèmes de grand ordre peut être très interessant de l'appliquer. La dernière partie est concentrée sur les observateurs à horizon glissant plus classiques et de traiter le cas où les hypothèses de régularité uniforme globale ne sont pas supposées. la description technique correspondante est donné à travers des définitions du rayon de régularité et du rayon d'observabilité.

Thèse de doctorat : Mathématiques : Tours : 2008. / Titre provenant de l'écran-titre.

Thesis (M.M.S.), Memorial University of Newfoundland, 2000. / Bibliography: leaves 131-137.

This thesis is devoted to creating a systematic way of determining all inequivalent orthogonal coordinate systems which separate the Hamilton-Jacobi equation for a given natural Hamiltonian defined on three-dimensional spaces of constant, non-zero curvature. To achieve this, we represent the problem with Killing tensors and employ the recently developed invariant theory of Killing tensors. Killing tensors on the model spaces of spherical and hyperbolic space enjoy a remarkably simple form; even more striking is the fact that their parameter tensors admit the same symmetries as the Riemann curvature tensor, and thus can be considered algebraic curvature tensors. Using this property to obtain invariants and covariants of Killing tensors, together with the web symmetries of the associated orthogonal coordinate webs, we establish an equivalence criterion for each space. In the case of three-dimensional spherical space, we demonstrate the surprising result that these webs can be distinguished purely by the symmetries of the web. In the case of three-dimensional hyperbolic space, we use a combination of web symmetries, invariants and covariants to achieve an equivalence criterion. To completely solve the equivalence problem in each case, we develop a method for determining the moving frame map for an arbitrary Killing tensor of the space. This is achieved by defining an algebraic Ricci tensor. Solutions to equivalence problems of Killing tensors are particularly useful in the areas of multiseparability and superintegrability. This is evidenced by our analysis of symmetric potentials defined on three-dimensional spherical and hyperbolic space. Using the most general Killing tensor of a symmetry subspace, we derive the most general potential “compatible” with this Killing tensor. As a further example, we introduce the notion of a joint invariant in the vector space of Killing tensors and use them to characterize a well-known superintegrable potential in the plane. xiii

Alexander Runciman was in his mid-thirties before he adopted the monumental style of history painting on which his reputation has always been held to rest. What may be called the formative part of his career was therefore unusually extended. This thesis is a study of his development during this time, its background, and the sources from which derived his ideas on painting. This part of his life culminated in the monumental paintings that he did for Sir James Clerk of Penicuik in 1772 and the related work in the Cowgate Chapel, Edinburgh. These were the most important of all his works and were unique in eighteenth century painting. In them he combined the grand style that he had learned during the four years that he spent in Rome, with the native Scottish tradition of decorative painting in which he had been trained. The thesis therefore falls into three parts. The first (Chaps.1-7) deals with his life and background in Edinburgh; the second (Chaps.8-15) with his four years in Rome; and the third (Chaps.16-18) with the works that he carried out on his return to Edinburgh. In the first part attention is given in Chapters 1 to 3 to the men of the older generation from whom he may have learnt not only his style, but also his ambitions as a painter. Chapters 4 and 5 deal with the circles in which he moved among his own contemporaries, and the last two chapters in this part with his own and his younger brother. John's work in Edinburgh before they left for Rome in 1767. In the second part the first three chapters(S-10) cover the brothers' stay in Rome up to John's death late in 1768, or early in 1769. Following this event Alexander became determined to succeed, not merely as a landscape and decorative painter, but in monumental history painting. Chapter 11 is a discussion of the work of Gavin Hamilton and of James Barry, the two painters who influenced him most at this time. This discussion is extended in Appendix D which deals more fully with the work of Gavin Hamilton. Chapters 12-14 are an account of Runciman's first works in the new manner, with particular attention to his proposals for the decoration of Penicuik House. Chapter 15 deals with his relationship to Henry Fuseli at the end of his Roman stay. The last three chapters give an account of the circumstances in which he finally carried out his work at Penicuik, and of the pictures themselves. As they were destroyed by fire in 1899 Chapter 18 and part of Chapter 19 are devoted to a reconstruction of their appearance. The thesis concludes with a discussion of his work in the Cowgate Chapel. The part of this which survives is all that is left of his monumental work.

There are over one thousand closed ‘small’ landfills in Ontario, each with differing circumstances and potential problems. This project proposes a method of addressing such dormant sites in situ, based upon a case study in Hamilton. Of the four closed landfills within Hamilton city limits, three of them lie in the low lands of the Red Hill Creek Valley. Perched at the source of the Red Hill Creek, the Upper Ottawa Street Landfill introduces unspoken toxins into the ecosystem of the entire valley. As the storm water catchment for the escarpment watershed, the creek serves a critical role in the recreational green belt which divides Hamilton and Stoney Creek. The source of this creek must be celebrated, not fenced off from public access due to landfill hazards. This proposal investigates beyond material recovery, into the possibilities of resource, ecosystem, and community recovery. Landfill mining, material sorting, and power generation through incineration are employed to reduce landfill volume. As the landfill is consumed, a new landscape is constructed, providing improved flood-prevention at the creek and a sanitary lined landfill for those materials remaining on site. Creek, forest, and field habitats are restored on site without the threat of contamination from landfill contents. The public can safely view the landfill mining operations from an elevated walkway, having new experiences with every visit. As the boundaries of the closed landfill are stripped away, the source of the Red Hill Creek and the new recreational parkland are made publicly accessible. Using this design as a reference, the equipment and operations designed for this site can be developed into a province-wide proposal.

Zugl.: Basel, Univ., Diss., 2003

>Magister Scientiae - MSc / Bank asset management mainly involves profit maximization through invest- ment in loans giving high returns on loans, investment in securities for reducing risk and providing liquidity needs. In particular, commercial banks grant loans to creditors who pay high interest rates and are not likely to default on their loans. Furthermore, the banks purchase securities with high returns and low risk. In addition, the banks attempt to lower risk by diversifying their asset portfolio. The main categories of assets held by banks are loans, treasuries (bonds issued by the national treasury), reserves and intangible assets. In this mini-thesis, we solve an optimal asset allocation problem in banking under the mean-variance frame work. The dynamics of the different assets are modelled as geometric Brownian motions, and our optimization problem is of the mean- variance type. We assume the Basel II regulations on banking supervision. In this contribution, the bank funds are invested into loans and treasuries with the main objective being to obtain an optimal return on the bank asset port- folio given a certain risk level. There are two main approaches to portfolio optimization, which are the so called martingale method and Hamilton Jacobi Bellman method. We shall follow the latter. As is common in portfolio op- timization problems, we obtain an explicit solution for the value function in the Hamilton Jacobi Bellman equation. Our approach to the portfolio prob- lem is similar to the presentation in the paper [Hojgaard, B., Vigna, E., 2007. Mean-variance portfolio selection and efficient frontier for defined contribution pension schemes. ISSN 1399-2503. On-line version ISSN 1601-7811]. We pro- vide much more detail and we make the application to banking. We illustrate our findings by way of numerical simulations.